A body of mass `m=10^(-2) kg` is moving in a medium and experiences a frictional force `F=-KUPSILON^(2).` Its initial speed is `upsilon_(0)=10ms^(-2)`. If , after `10s`, its energy is `(1)/(8)m upsilon_(0)^(2)`, the value of `k` will be

Options

A. `10^(-4) kg m^(-1)`
B. `10^(-1)kg m^(-1)`
C. `10^(-3)kg m^(-1)`
D. `10^(-3)kg m^(-1)`

Explanation

To solve the problem, we need to find the value of \( k \) given the mass \( m = 10^{-2} \, \text{kg} \), initial speed \( v_0 = 10 \, \text{m/s} \), and the final energy after \( 10 \, \text{s} \) is \( \frac{1}{8} m v_0^2 \).

### Step-by-Step Solution:

1. **Calculate Initial Energy:**
The initial kinetic energy \( KE_0 \) of the body is given by the formula:
\[
KE_0 = \frac{1}{2} m v_0^2
...